What is the answer to 3^x(5^{2x})=6(2^x) ?

The answer to 3^x(5^{2x})=6(2^x) is x=(ln(6))/(ln(75)-ln(2))

Solve for x: 3^x(5^{2x})=6(2^x)

The solution is x=(ln(6))/(ln(75)-ln(2))

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3^{x} (5^{2 x}) = 6 (2^{x})

x = \frac{ln ( 6 )}{ln ( 75 ) - ln ( 2 )}

Decimal Notation

x = 0.49436 \dots

Solution steps

3^{x} (5^{2 x}) = 6 (2^{x})

Apply exponent rules

(lo g_{2} (3) x + lo g_{2} (5) \cdot 2 x) ln (2) = ln (6) + x ln (2)

Solve

(lo g_{2} (3) x + lo g_{2} (5) \cdot 2 x) ln (2) = ln (6) + x ln (2) : x = \frac{ln ( 6 )}{ln ( 75 ) - ln ( 2 )}

x = \frac{ln ( 6 )}{ln ( 75 ) - ln ( 2 )}

2^{x} - 2^{x - 2} = 6

1 0^{2 - b} = 10000

\frac{2 7 ^{2}}{8 1 ^{3}} = 3^{x}

2 e^{x} - 9 e^{- 3 x} = 0

(\frac{4}{3})^{1 - x} = 5^{x}

What is the answer to 3^x(5^{2x})=6(2^x) ?
The answer to 3^x(5^{2x})=6(2^x) is x=(ln(6))/(ln(75)-ln(2))
Solve for x: 3^x(5^{2x})=6(2^x)
The solution is x=(ln(6))/(ln(75)-ln(2))